Problem: Vanessa decided to paint some of the rooms at her 19-room inn, Vanessa's Place. She discovered she needed $\frac{3}{5}$ of a can of paint per room. If Vanessa had 6 cans of paint, how many rooms could she paint?
Solution: We can divide the cans of paint (6) by the paint needed per room ( $\frac{3}{5}$ of a can) to find out how many rooms Vanessa could paint. $ \dfrac{{6 \text{ cans of paint}}} {{\dfrac{3}{5} \text{ can per room}}} = {\text{ rooms}} $ Dividing by a fraction is the same as multiplying by the reciprocal. The reciprocal of ${\dfrac{3}{5} \text{ can per room}}$ is ${\dfrac{5}{3} \text{ rooms per can}}$ $ {6\text{ cans of paint}} \times {\dfrac{5}{3} \text{ rooms per can}} = {\text{ rooms}} $ ${\dfrac{30}{3}\text{ rooms}} = 10\text{ rooms}$ Vanessa could paint 10 rooms.